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Chapter 3: Problem 150

A lift is moving down with an acceleration \(a\). A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are, respectively, (A) \(g, g\) (B) \(g-a, g,-a\) (C) \(g-a, g\) (D) \(a, g\)

Short Answer

Expert verified
The short answer is: The acceleration of the ball as observed by the man inside the lift is \(g-a\) and the acceleration of the ball as observed by the man on the ground is \(g + a\). The best choice is (C) \(g-a, g\).

Step by step solution

01

Consider the man inside the lift as the observer

From the perspective of the man inside the lift, the ball is acted upon by only the gravitational force with acceleration \(g\). Since the lift is moving downward with acceleration \(a\) and the ball is moving along with it, the man inside the lift will observe the ball as having an acceleration of \(g-a\).
02

Consider the man on the ground as the observer

For the man standing stationary on the ground, the ball is acted upon by two forces: the gravitational force and the downward acceleration of the lift. Therefore, the man on the ground will observe the ball falling with an acceleration of \(g + a\) (since downward motion is considered negative).
03

Identify the correct answer

Based on our analysis, the acceleration of the ball as observed by the man inside the lift is \(g-a\) and the acceleration of the ball as observed by the man on the ground is \(g + a\). Comparing our results with the given options, we can see that none of the options exactly match our findings. However, option (C) is partially correct, as it correctly states the acceleration observed by the man inside the lift. Since none of the other options are more accurate, we can consider option (C) as the best choice. So, the answer is (C) \(g-a, g\).

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Most popular questions from this chapter

A man of mass \(70 \mathrm{~kg}\) stands on a weighing scale in lift which is moving. Choose the correct statement. (A) Reading of weighing scale is \(700 \mathrm{~N}\) upwards with a uniform speed of \(10 \mathrm{~ms}^{-1}\). (B) Reading of weighing scale is \(700 \mathrm{~N}\) downwards with a uniform acceleration of \(5 \mathrm{~ms}^{-2}\) (C) Reading of weighing scale is \(700 \mathrm{~N}\) upwards with a uniform acceleration of \(5 \mathrm{~ms}^{-2}\) (D) Reading of weighing scale is \(700 \mathrm{~N}\) if the lift mechanism failed and it fall down freely under gravity.

The angular velocity of a wheel increases from 1200 rpm to 4500 rpm in \(10 \mathrm{~s}\). The number of revolutions made during this time is (A) 950 (B) 475 (C) \(237.5\) (D) \(118.75\)

A pebble of mass \(0.05 \mathrm{~kg}\) is thrown vertically upwards. The direction and magnitude of the net force on the pebble is given below, choose the incorrect option. (A) During its upward motion, force is \(0.5 \mathrm{~N}\) in vertically upward. (B) During its downward motion, force is \(0.5 \mathrm{~N}\) in vertically downward. (C) At the highest point, where it is momentarily at rest, force is \(0.5 \mathrm{~N}\) in vertically downward. (D) If the pebble was thrown at an angle of say \(45^{\circ}\) with the horizontal direction, force is \(0.5 \mathrm{~N}\) in vertically downward (Ignoring air resistance).

A body of mass \(2 \mathrm{~kg}\) moves vertically downwards with an acceleration \(a=19.6 \mathrm{~m} / \mathrm{s}^{2}\). The force acting on the body simultaneously with the force of gravity is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right.\), neglect air resistance) (A) \(19.6 \mathrm{~N}\) (B) \(19.2 \mathrm{~N}\) (C) \(59.2 \mathrm{~N}\) (D) \(58.8 \mathrm{~N}\)

Two masses \(8 \mathrm{~kg}\) and \(12 \mathrm{~kg}\) are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the tension the string when the masses are released. (A) \(96 \mathrm{~N}\) (B) \(80 \mathrm{~N}\) (C) \(100 \mathrm{~N}\) (D) None of these
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